Angioplasty balloons are widely used to dilate stenosed regions of blood vessels. Typical practice is to increase the inflation pressure in the balloon at the stenosed region until the vessel yields and optimal blood flow has been restored. In some instances, however, the inflation pressure may be increased to such a degree that the balloon bursts. If the balloon fails or tears longitudinally and remains in one piece, the burst may not be particularly problematic. If, on the other hand, a longitudinal tear propagates to the taper or neck of the balloon and changes direction, the balloon may experience a “radial burst” and fragment into two or more pieces. The resulting balloon fragments may be embolized and remain in the vessel even after the balloon catheter has been withdrawn, potentially threatening the health of the patient.